# Gentle Sum

Calculus Level 4

$\large \lim_{n\to\infty} \dfrac1{4n^2} \sum_{k=1}^n \sqrt{4n^2-k^2}$

If the limit above equals to $$\dfrac{\pi}P + \dfrac {\sqrt 3}R$$ for positive integers $$P$$ and $$R$$, find the value of $$P + R$$.

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